In wavelength division multiplexed (WDM) optical communication systems, a number of different optical carrier wavelengths are separately modulated with data to produce modulated optical signals. The modulated optical signals are combined into an aggregate signal and transmitted over an optical transmission path to a receiver. The receiver detects and demodulates the data.
One type of modulation that may be used in optical communication systems is phase shift keying (PSK). According to different variations of PSK, data is transmitted by modulating the phase of an optical wavelength such that the phase or phase transition of the optical wavelength represents symbols encoding one or more bits. In a binary phase-shift keying (BPSK) modulation scheme, for example, two phases may be used to represent 1 bit per symbol. In a quadrature phase-shift keying (QPSK) modulation scheme, four phases may be used to encode 2 bits per symbol. Other phase shift keying formats include differential phase shift keying (DPSK) formats and variations of PSK and DPSK formats, such as return-to-zero DPSK (RZ-DPSK) and phase division multiplexed QPSK (PDM-QPSK).
A modulation format, such as QPSK wherein multiple data bits are be encoded on a single transmitted symbol may be generally referred to as a multi-level modulation format. Multi-level modulation techniques have been used, for example, to allow increased transmission rates and decreased channel spacing, thereby increasing the spectral efficiency (SE) of each channel in a WDM system. One spectrally efficient multi-level modulation format is quadrature amplitude modulation (QAM). In a QAM signal, information is modulated using a combination of phase shift keying and amplitude shift keying, for example, to encode multiple bits per symbol. A 16-QAM modulation format may be used, for example, to encode 4 bits per symbol. Certain PSK modulation schemes (e.g., BPSK and QPSK) may be referred to as a level of QAM (e.g., 2 QAM and 4 QAM respectively).
One problem associated with optical communication systems is maintaining the integrity of the data being communicated, particularly when optical signals are transmitted over long distances in long-haul communication systems. Accumulated noise contributed by many different sources in a transmission path may cause degradation of the signals and may cause difficulty in differentiating between the binary digits (i.e., the ones and zeros) in a data stream.
Forward Error Correction (FEC) is a technique used to help compensate for this degradation. FEC is essentially the incorporation of a suitable code into a data stream at the transmitter. The transmitter receives a data stream and encodes the data stream using an FEC encoder that introduces some redundancy in the binary information sequence of the data stream. The receiver receives the encoded data and runs it through an FEC decoder to detect and correct errors.
Gray mapping has also been applied to achieve improvements in detection. Gray mapping is a known process wherein a non-weighted code is assigned to each of a contiguous set of bits such that adjacent code words differ by one symbol, i.e. they have a Hamming distance of 1. For example, in a 16 QAM system where data is transmitted in symbols representing 4-bits the constellation diagram of the signal is arranged with Gray mapping such that Gray coded patterns of 4-bits conveyed by adjacent constellation points differ by only one bit. Combining Gray mapping with FEC can facilitate correction of transmission errors that cause a constellation point in the signal constellation diagram to deviate into the area of an adjacent point.
One approach to combining data modulation with FEC coding is known as bit-interleaved coded-modulation (BICM). In a BICM scheme FEC coding is applied to a data stream and the FEC coded data stream is then bit-interleaved (i.e. the order of the bits is permuted). The coded and interleaved data stream is then modulated according to a selected data modulation with, or without, Gray mapping. The performance of BICM can be further increased in some cases by exchanging information between the de-mapper and the decoder and performing iterative decoding (ID). BICM schemes with ID decoding are known as BICM-ID schemes.
It has been found, however, that the performance of BICM with Gray mapping may be limited. BICM-ID without Gray mapping can actually outperform BICM with Gray mapping for some FEC codes and may achieve vanishing error probability with iterative decoding. For other FEC codes, however, BICM-ID without Gray mapping may still outperform BICM with Gray mapping, but performance improvements diminish with iterative decoding so that essentially error-free decoding is not achieved.